Wykorzystanie modelu różnicowego do analizy cykliczności wydatków budżetu państwa w zależności od dochodów - Janiga-Ćmiel, Anna (Application of Differential Model to the Analysis of Revenue-Based State Budget Expenditure Periodicity, 2006)
Complex economic phenomena develop as time passes consistently with a fixed function of the trend around which some regular or irregular oscillations occur. Regular oscillations occur periodically, however in the case of the state budget and other variables characterizing variability of the economic situation in a global way, they have variable amplitudes and variable consecutive periods of cycles. They can be detected using differential or difference equations. Square different equations with complex characteristic roots were used in this work. Solutions of a characteristic equation are complex numbers because the examined phenomenon, which is the economic situation, shows oscillations. It is necessary to introduce trigonometric functions into the trigonometric model. Their sum allows to determine the oscillation amplitude variable within consecutive cycles as well as variable lengths of consecutive cycles.Moreover, it is possible to estimate a prognosis of amplitudes and the length of periods of cycles for future cycles. In the solution of the equation, except a specific solution presented in the trigonometric form, we obtain a general solution which constitutes a function of the trend of the phenomenon examined. The form of the trend function is precisely adjusted to the phenomenon in question and there is no better method to determine it.To sum up, thorough examination of the periodisation of the phenomenon is a priority for the decision-making process in management. On the other hand, results of this work can be practically used to make a right decision.
Prace Naukowe Akademii Ekonomicznej we Wrocławiu; 2006; nr 1117, s. 49-57